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Class 8 Maths Worksheet: Squares and Square Roots

Maths worksheets lesson 58: Squares and square roots · Set 446 · 40 sums
TalentJR

The method (Pairs make squares): Square: n × n. Quick way: (a + b)² = a² + 2ab + b², e.g. 42² = 1600 + 160 + 4. Square root: the number that times itself gives the square; a square ending in 4 has a root ending in 2 or 8. Make a perfect square: break into primes; multiply (or divide) by the prime left without a partner. 1 + 3 + 5 + … (n odd numbers) = n². Between n² and (n + 1)² there are 2n whole numbers.

NameDateTime takenScore ___ / 40
  1. 1.What is the smallest whole number by which 90 must be multiplied to get a perfect square?
  2. 2.Which of these is a perfect square? (a) 850 (b) 862 (c) 841
  3. 3.How many whole numbers lie between 45² and 46²?
  4. 4.What is 39²? =
  5. 5.What is √2304? =
  6. 6.What is the smallest whole number by which 180 must be multiplied to get a perfect square?
  7. 7.How many whole numbers lie between 28² and 29²?
  8. 8.A square garden has an area of 3364 square m. How long is each side (in m)?
  9. 9.A square garden has an area of 361 square m. How long is each side (in m)?
  10. 10.Which of these is a perfect square? (a) 100 (b) 110 (c) 115
  11. 11.What is √7569? =
  12. 12.What is the smallest whole number by which 20 must be multiplied to get a perfect square?
  13. 13.Which of these is a perfect square? (a) 184 (b) 172 (c) 169
  14. 14.What is the smallest whole number by which 18 must be divided to get a perfect square?
  15. 15.A square garden has an area of 3600 square m. How long is each side (in m)?
  16. 16.How many whole numbers lie between 38² and 39²?
  17. 17.What is the smallest whole number by which 208 must be multiplied to get a perfect square?
  18. 18.Which of these is a perfect square? (a) 235 (b) 237 (c) 225
  19. 19.What is √5476? =
  20. 20.Which of these is a perfect square? (a) 400 (b) 404 (c) 412
  21. 21.What is √2704? =
  22. 22.How many whole numbers lie between 41² and 42²?
  23. 23.What is √2601? =
  24. 24.What is √529? =
  25. 25.What is √4761? =
  26. 26.What is the smallest whole number by which 54 must be divided to get a perfect square?
  27. 27.What is 79²? =
  28. 28.What is the sum of the first 6 odd numbers (1 + 3 + 5 + …)?
  29. 29.A square garden has an area of 576 square m. How long is each side (in m)?
  30. 30.What is the smallest whole number by which 45 must be divided to get a perfect square?
  31. 31.What is the sum of the first 24 odd numbers (1 + 3 + 5 + …)?
  32. 32.What is the smallest whole number by which 350 must be multiplied to get a perfect square?
  33. 33.Which of these is a perfect square? (a) 543 (b) 529 (c) 540
  34. 34.What is √1369? =
  35. 35.What is √3364? =
  36. 36.What is the smallest whole number by which 735 must be multiplied to get a perfect square?
  37. 37.What is the smallest whole number by which 24 must be multiplied to get a perfect square?
  38. 38.What is 32²? =
  39. 39.How many whole numbers lie between 7² and 8²?
  40. 40.What is √4356? =

Answer key

  1. 10
  2. 841
  3. 90
  4. 1521
  5. 48
  6. 5
  7. 56
  8. 58
  9. 19
  10. 100
  11. 87
  12. 5
  13. 169
  14. 2
  15. 60
  16. 76
  17. 13
  18. 225
  19. 74
  20. 400
  21. 52
  22. 82
  23. 51
  24. 23
  25. 69
  26. 6
  27. 6241
  28. 36
  29. 24
  30. 5
  31. 576
  32. 14
  33. 529
  34. 37
  35. 58
  36. 15
  37. 6
  38. 1024
  39. 14
  40. 66

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